That being said, I have "a thing" about replaying single-player narrative games. Since I fancy myself a connoisseur (full disclosure: spellcheck helped me out on that word) of the interactive arts, I have it in my head that I need to be constantly broadening my pallet, so to speak. Of course there's nothing wrong with replaying games, and in fact games in their purest form are meant to be re-played. Still, I think there's something to be said for trying new things.
In the last two years I have taken to buying used games at a rate that far exceeds my capacity to play them. I'm not really averse to playing decade-old games for the first time (this year I've played and finished Metal Gear Solid 2, Chrono Trigger, and Metroid Zero Mission, amongst others), so after my recent purchase of Portal 2 I set a temporary rule for myself:
I'm not allowed to buy another game until I beat ten games that I own but haven't beaten before.
I'm willing to be flexible, of course, since some games don't focus on their "completed state" (i.e. Rock Band 3) and others perhaps have unrealistic goals for theirs (i.e. Pokemon Black). That being said, I need some help sorting through the stockpile of games I've amassed. That's where you come in! Help me choose games! See anything that sets off a wave of nostalgia? Want to play through any of these alongside me? Let me know!
In no particular order, the list of games I own that I should probably play:
Left 4 Dead 2
StarCraft
Braid
Machinarium (pictured)
StarFox: Command
Final Fantasy Tactics A2: Grimoire of the Rift
Gish
Aurora

Monday Night Combat (pictured)
Cortex Command
Osmos
World of Goo
Penumbra
Aquaria
Lugaru

Time, Gentlemen, Please!
Revenge of the Titans
Rayman (pictured)
Chrono Cross
Elder Scrolls - Daggerfall
Nier
Okami

The Darkness
Deus Ex
Eternal Darkness (pictured)
Dragon Quest VII: Journey of the Cursed King
Shadow of the Colossus
Link's Crossbow Training
Psychonauts
The Legend of Zelda: Phantom Hourglass
Skies of Arcadia Legends
Rayman 2: The Great Escape
Banjo-Tooie
Star Wars Jedi Knight: Jedi Academy
Red Dead Redemption (pictured)
Rock Band 3
Borderlands
NBA Jam
Starfox
Baten Kaitos
XIII
Viewtiful Joe (pictured)
Lost Odyssey
Super Mario Galaxy 2
Fallout 3
Lego Indiana Jones
Dragon Quest IV: Chapters of the Chosen
Retro Game Challenge (pictured)
Breath of Fire II
Zack and Wiki: The Quest for Barbaros' Treasure
Tales of Symphonia
Golden Sun: The Lost Age
The Legend of Zelda
Zelda II: The Adventure of Link
Sonic & Knuckles
I completed Portal 2's single-player campaign (excellent! great fun) and I'm looking forward to the rest of the co-op. That will be game one of ten!